Image restoration is the process of estimating an image from a corrupted image that has undergone some degradation such as blur or additive noise. To perform any sort of image restoration, knowledge of the degradation process is required. In the absence of information about the imaging system that was used to capture a given degraded image, the degradation has to be estimated directly from the degraded image itself; this type of estimation is known as blind estimation.
Blur degradation of an image is typically modelled as the interaction of the un-degraded image with a blurring function called the blur kernel, the form of this interaction being, for example, expressed as the convolution, in the spatial domain, of the blur kernel with the pixels of the un-degraded image.
Previous approaches to blind estimation of blur degradation typically assume frequency domain constraints on images or a simplified parametric form for the blur kernel shape. However, real-world blurs are usually much more complicated, often contain high frequency components and only rarely can be accommodated by functions that contain a small number of parameters. For example, although the blur kernels that are induced by camera shake are complicated and may contain convoluted paths, motion is often assumed to be linear (i.e., the blur kernel is characterized solely by angle and size). Similarly while focal blur is often modelled as a simple circular disk or a low frequency Fourier component (e.g., a normalized Gaussian function), in practice the blur kernel shape is far more elaborate and may contain sharp edges.
Several blur estimation methods have been proposed in the literature which are based on the estimation of the blur function from a degraded ideal step-edge (for example, see the paper: “Blind Restoration of Atmospherically Degraded Images by Automatic Best Step-Edge Detection” O. Shacham, O. Haik and Y. Yitzaky). Usually the ideal step-edge is a high contrast straight edge that is long enough so that noise will be averaged over a large area; high contrast and straight edges are sought because they yield better signal to noise ratio and because they are common and relatively reliable for analysis. From each such degraded ideal step-edge it is then possible to estimate the projection of the blur kernel in the direction of the considered edge. Unfortunately, even if several edges running in different directions are taken into account, it is very difficult to derive the blur kernel accurately.